Tiafoe needed more than two hours and four match points to complete the win over 10th seed Musetti on a humid night in Ohio, with nearby thunderstorms threatening but never interrupting play.
Tiafoe, seeking to revive a summer disrupted by early exits in Washington and Montreal as well as a wrist injury, played aggressively throughout, firing 18 winners before sealing victory with an unreturnable serve.
Check out the full matchup stats here.
Tiafoe owns a 6-1 career record against Nakashima but will face a player in confident form after Nakashima rallied from a break down in the deciding set to beat fellow American and sixth seed Taylor Fritz 7-6(9) 4-6 6-3.
Nakashima has now reached the last four at back-to-back Masters 1000 events after his run in Montreal last week, capping another impressive turnaround on the North American hard courts ahead of the U.S. Open, which starts later this month.